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Number of Teeth on Helical Gear is defined as the number of teeth (which mesh with another compatible toothed part to transmit or convert torque and speed) on a specimen or part under consideration. Check FAQs
z=dcos(ψ)mn
z - Number of Teeth on Helical Gear?d - Diameter of Pitch Circle of Helical Gear?ψ - Helix Angle of Helical Gear?mn - Normal Module of Helical Gear?

Number of Teeth on Gear given Pitch Circle Diameter Example

With values
With units
Only example

Here is how the Number of Teeth on Gear given Pitch Circle Diameter equation looks like with Values.

Here is how the Number of Teeth on Gear given Pitch Circle Diameter equation looks like with Units.

Here is how the Number of Teeth on Gear given Pitch Circle Diameter equation looks like.

35.6481Edit=118Editcos(25Edit)3Edit
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Number of Teeth on Gear given Pitch Circle Diameter Solution

Follow our step by step solution on how to calculate Number of Teeth on Gear given Pitch Circle Diameter?

FIRST Step Consider the formula
z=dcos(ψ)mn
Next Step Substitute values of Variables
z=118mmcos(25°)3mm
Next Step Convert Units
z=0.118mcos(0.4363rad)0.003m
Next Step Prepare to Evaluate
z=0.118cos(0.4363)0.003
Next Step Evaluate
z=35.6481062901096
LAST Step Rounding Answer
z=35.6481

Number of Teeth on Gear given Pitch Circle Diameter Formula Elements

Variables
Functions
Number of Teeth on Helical Gear
Number of Teeth on Helical Gear is defined as the number of teeth (which mesh with another compatible toothed part to transmit or convert torque and speed) on a specimen or part under consideration.
Symbol: z
Measurement: NAUnit: Unitless
Note: Value should be greater than 0.
Diameter of Pitch Circle of Helical Gear
Diameter of Pitch Circle of Helical Gear is the diameter of the pitch circle of a gear that touches the meshing gear's pitch circle.
Symbol: d
Measurement: LengthUnit: mm
Note: Value should be greater than 0.
Helix Angle of Helical Gear
Helix Angle of Helical Gear is the angle between any helical gear and an axial line on its right, circular cylinder, or cone.
Symbol: ψ
Measurement: AngleUnit: °
Note: Value should be greater than 0.
Normal Module of Helical Gear
The Normal Module of Helical Gear is defined as the unit of size that indicates how big or small is the helical gear.
Symbol: mn
Measurement: LengthUnit: mm
Note: Value should be greater than 0.
cos
Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.
Syntax: cos(Angle)

Other Formulas to find Number of Teeth on Helical Gear

​Go Number of Teeth on Helical Gear given Speed Ratio for Helical Gears
z=Zpi
​Go Number of Teeth on Gear given Addendum Circle Diameter
z=(damn-2)cos(ψ)
​Go Actual Number of Teeth on Gear given Virtual Number of Teeth
z=(cos(ψ))3z'

Other formulas in Core Design Parameters category

​Go Transverse Module of Helical Gear given Transverse Diametrical Pitch
m=1P
​Go Normal Module of Helical Gear
mn=mcos(ψ)
​Go Transverse Module of Helical Gear given Normal Module
m=mncos(ψ)
​Go Pitch Circle Diameter of Helical Gear
d=zmncos(ψ)

How to Evaluate Number of Teeth on Gear given Pitch Circle Diameter?

Number of Teeth on Gear given Pitch Circle Diameter evaluator uses Number of Teeth on Helical Gear = Diameter of Pitch Circle of Helical Gear*cos(Helix Angle of Helical Gear)/Normal Module of Helical Gear to evaluate the Number of Teeth on Helical Gear, The Number of Teeth on Gear given Pitch Circle Diameter formula is defined as the number of protrusions onto the periphery of a gear that mesh with teeth of another gear to transmit motion. Number of Teeth on Helical Gear is denoted by z symbol.

How to evaluate Number of Teeth on Gear given Pitch Circle Diameter using this online evaluator? To use this online evaluator for Number of Teeth on Gear given Pitch Circle Diameter, enter Diameter of Pitch Circle of Helical Gear (d), Helix Angle of Helical Gear (ψ) & Normal Module of Helical Gear (mn) and hit the calculate button.

FAQs on Number of Teeth on Gear given Pitch Circle Diameter

What is the formula to find Number of Teeth on Gear given Pitch Circle Diameter?
The formula of Number of Teeth on Gear given Pitch Circle Diameter is expressed as Number of Teeth on Helical Gear = Diameter of Pitch Circle of Helical Gear*cos(Helix Angle of Helical Gear)/Normal Module of Helical Gear. Here is an example- 35.64811 = 0.118*cos(0.4363323129985)/0.003.
How to calculate Number of Teeth on Gear given Pitch Circle Diameter?
With Diameter of Pitch Circle of Helical Gear (d), Helix Angle of Helical Gear (ψ) & Normal Module of Helical Gear (mn) we can find Number of Teeth on Gear given Pitch Circle Diameter using the formula - Number of Teeth on Helical Gear = Diameter of Pitch Circle of Helical Gear*cos(Helix Angle of Helical Gear)/Normal Module of Helical Gear. This formula also uses Cosine (cos) function(s).
What are the other ways to Calculate Number of Teeth on Helical Gear?
Here are the different ways to Calculate Number of Teeth on Helical Gear-
  • Number of Teeth on Helical Gear=Number of Teeth on Helical Pinion*Helical Gear Speed RatioOpenImg
  • Number of Teeth on Helical Gear=(Addendum Circle Diameter of Helical Gear/Normal Module of Helical Gear-2)*cos(Helix Angle of Helical Gear)OpenImg
  • Number of Teeth on Helical Gear=(cos(Helix Angle of Helical Gear))^(3)*Virtual Number of Teeth on Helical GearOpenImg
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